Perspectives on Borges’ Library of Babel CJ Fearnley Jeannie Moberly cjf@CJFearnley.com moberlypj@yahoo.com http://www.CJFearnley.com http://Moberly.CJFearnley.com 240 Copley Road Upper Darby, PA 19082, USA 29 July 2015 Presentation to Bridges Baltimore 2015 : Mathematics, Music, Art, Architecture, Culture at The University of Baltimore in Baltimore, MD, USA Landing Page for our work on Harmonic Perspective: http://www.CJFearnley.com/HarmonicPerspective
Borges’ Library of Babel Background: Harmonics and Perspective Our 2012 Bridges paper: “Harmonic Perspective” This work continues our 2012 Bridges paper on “Harmonic Perspective” with two new geometrical variants on harmonics: harmonic sequences and nets of rationality and a pencil of nonintersecting Apollonian circles. Perspectives on Borges’ Library of Babel CJ Fearnley/Jeannie Moberly, Math/Art
Borges’ Library of Babel Background: Harmonics and Perspective Perspectivism In a free on-line course on Dante, Giuseppe Mazzotta defines perspectivism as “a way of assembling various points of view.” Perspective may be important: knowing, doing, and perceiving may be subject to both its power for seeing and its biases. How can artists move beyond the limiting form of perspective developed by Renaissance artists and abstracted into the science of projective geometry by mathematicians? Perspectives on Borges’ Library of Babel CJ Fearnley/Jeannie Moberly, Math/Art
Borges’ Library of Babel Jeannie’s Artwork and Borges’ Library The Library of Babel This work explores a new subject in the form of The remarkable “Universe (which others call the Library)” described in “The Library of Babel” by Jorge Luis Borges (1941). The Library consists of a vast number of rooms each with the same number of books, airshafts, staircases, and anterooms. The librarians wander their whole lives through the labyrinth of rooms wondering about the nature of their Universe. Many aspects of the Library are left open to speculation. Perspectives on Borges’ Library of Babel CJ Fearnley/Jeannie Moberly, Math/Art
Borges’ Library of Babel Jeannie’s Artwork and Borges’ Library The Unimaginable Mathematics of Borges’ Library of Babel William Goldbloom Bloch’s great book is an accessible, fun survey of the mathematical surprises lurking in The Library. Perspectives on Borges’ Library of Babel CJ Fearnley/Jeannie Moberly, Math/Art
Borges’ Library of Babel Jeannie’s Artwork and Borges’ Library View of Apollonian Ventilation Shafts Perspectives on Borges’ Library of Babel CJ Fearnley/Jeannie Moberly, Math/Art
Borges’ Library of Babel Jeannie’s Artwork and Borges’ Library Another View of “Borges’ Library of Babel” Perspectives on Borges’ Library of Babel CJ Fearnley/Jeannie Moberly, Math/Art
Borges’ Library of Babel Harmonic Sequences and Nets of Rationality A Harmonic Sequence: Constructing the Integers Geometrically Perspectives on Borges’ Library of Babel CJ Fearnley/Jeannie Moberly, Math/Art
Borges’ Library of Babel Harmonic Sequences and Nets of Rationality Nets of Rationality By adding, multiplying and dividing the points of a harmonic sequence geometrically, any rational number can be constructed. By producing another harmonic sequence (which may be metrically incommensurable with the first) on another distinct line and aligning the two lines with a shared point, a planar net of rationality may be developed. Repeat again for a “net of rationality” in 3-space. Jeannie used such nets to “measure” the space in laying out “Borges’ Library of Babel” Perspectives on Borges’ Library of Babel CJ Fearnley/Jeannie Moberly, Math/Art
Borges’ Library of Babel The Non-Intersecting Pencil of Apollonian Circles Constructing a Pencil of Apollonian Circles Perspectives on Borges’ Library of Babel CJ Fearnley/Jeannie Moberly, Math/Art
Borges’ Library of Babel The Non-Intersecting Pencil of Apollonian Circles Apollonian Circles in “Borges’ Library of Babel” Apollonian circles are used to represent the layout of the rooms and ventilation shafts in The Library. Perspectives on Borges’ Library of Babel CJ Fearnley/Jeannie Moberly, Math/Art
Borges’ Library of Babel Conclusion and Questions Conclusion and Questions An artwork is a tool for the imagination. Jeannie’s “Borges’ Library of Babel” and Borges’ short story both provide tools for us to imagine the ethereal concepts of the enormous but finite and the infinite and the infinitely periodic suggested at the end of Borges’ story and in Bloch’s in analysis of “The Grand Pattern”. Can the concrete incidences in harmonic constructions engage us in imagining the wild abstractions of The Library? Can the unknowable, the unimaginable and the ineffable be represented artistically? How can we assemble these points of view? How can we get perspective on perspective? Perspectives on Borges’ Library of Babel CJ Fearnley/Jeannie Moberly, Math/Art
Borges’ Library of Babel Conclusion and Questions Thank You Thank You! Any Questions? Landing Page for our our work on Harmonic Perspective including our Bridges 2012 Paper & Presentation: http://www.CJFearnley.com/HarmonicPerspective Perspectives on Borges’ Library of Babel CJ Fearnley/Jeannie Moberly, Math/Art
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